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Pre-Calculus Conics Review Name __________________________________
March 2014 Graph the ellipse and identify the center, vertices, and foci.
1.
2.
Center:___________ Center:___________
Vert:__________ Vert:__________
Foci:________ Foci:________
3. 4.
Center:___________ Center:___________
Vert:__________ Vert:__________
Foci:________ Foci:________
5. ( )
( )
6. ( ) ( )
Center:___________ Center:___________
Vert:__________ Vert:__________
Foci:________ Foci:________
Find the standard form of the equation of each ellipse.
7. Foci (0, 3), vertices (0, 5) 8. Major axis horizontal with length 12; length of minor axis 4; center: (- 1, 3) 9. Foci ( 5, 0), length of major axis 12 10. Endpoints of major axis: (2, 2) & (8, 2) Endpoints of minor axis: (5, 3) & (5, 1)
11. 12.
Convert each equation to standard form by completing the square. 13. 14. Graph the hyperbola and identify the center, vertices, asymptotes, and foci.
15.
16.
Center: ___________ Center: ___________
Vertices:___________ Vertices:___________
Foci:__________ Foci:__________
Asymptotes:________ Asymptotes:________
17. ( ) ( ) 18. ( )
( )
Center:____________ Center: ____________
Vertices:___________ Vertices:___________
Foci:__________ Foci:__________
Asymptotes:________ Asymptotes:________
19. ( )
( )
20.
( )
–
( )
Center: ___________ Center: ___________
Vertices:___________ Vertices:___________
Foci:__________ Foci:__________
Asymptotes:________ Asymptotes:________
Find the standard form of the equation of each hyperbola.
21. Foci (0, 4), vertices (0, 2) 22. Vertices ( 4, 0), Asymptotes:
23. Endpoints of transverse axis: (0, ) 24. Foci (0, 1), length of transverse axis 1 Asymptotes: y = x
25. 26.
𝒚 𝟑𝒙
𝒚 𝟑𝒙
Convert each equation to standard form by completing the square.
27. 28.
Graph the parabola and identify the vertex, directrix, and focus.
29. 30.
Vertex: _______ Vertex: _______
Dir: _______ Dir: ____________
Focus: ___________ Focus:_________
31. ( ) ( ) 32. ( )
Vertex: _______ Vertex: _______
Dir: ___________ Dir: __________
Focus: ________ Focus:________
33. ( ) ( ) 34. ( )
Vertex: _______ Vertex: _______
Dir: _______ Dir: ____________
Focus: ___________ Focus:_________
Write an equation in standard form for the parabola satisfying the given conditions.
35. Focus: (9, 0); Directrix: x = -9 36. Focus: (-10, 0); Directrix: x = 10
37. Vertex: (5, -2); Focus (7, -2) 38. Focus: (2, 4); Directrix: x = -4
Find the equation for the parabola whose graph is shown.
39. 40.
Convert each equation to standard form by completing the square.
41. 42.
F(0, -3)
Answers:
1. C(0, 0); V(0, ± 5); F(0, ± 4) 2. C(0, 0); V(± 5, 0); F( √ )
3. C(0, 0); V(± 6, 0); F( √ , 0) 4. C(0, 0); V(0, ± 2); F(0, √ )
5. C(1, -2); V(1, 1); (1, -5); F(1, -2 √ ) 6. C(-4, -3); V(-4, 3); (-4, -9); F(-4, -3 √ )
7.
8.
( )
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10.
( )
( )
11.
12.
( )
( )
13.
( )
( )
14.
( )
( )
15. C(0, 0); V(0, ± 3); F(0, ± 5); T: y =
16. C(0, 0); V(± 2, 0); F(± √ , 0); T: y =
17. C(1, -2); V(-2, -2) ; (4, -2); F(1 ± √ , -2); T: y + 2=
( )
18. C(2, -1); V(2, 4) ;(2, -6); F(2, -1 ± √ ); T: y + 1=
(x-2)
19. C(3, -2); V(3, 3) ; (3, -7); F(3, -2 ± √ ); T: y + 2=
(x-3)
20. C(2, -3); V(-3, -3) ; (7, -3); F(2 ± √ , -3); T: y+3=
(x-2)
21.
22.
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24.
⁄
⁄
25. ( )
( )
26.
27.
( )
( )
28.
( )
( )
29. V(0, 0); Dir: x = 3; F(-3, 0) 30. V(0, 0); Dir: y = - 2; F(0, 2) 31. V(-1, 3); Dir: y =
; F(-1,
)
32. V(-2, 0); Dir: x = - 5; F(1, 0) 33. V(-2, -2); Dir: y = 0; F(-2, -4) 34. V(0, 1); Dir: x = 2; F(-2, 1) 35. y2 = 36x 36. y2 = -40x 37. (y+2)2 = 8(x-5) 38. (y-4)2 = 12(x+1) 39. y2 = 8x 40. x2 = -12y 41. (x+3)2 = -8(y-1) 42. (y+4)2 = 4(x+2)